Mr Rajan took over the reins of the RBI at a time when India's economy was struggling with a ballooning current account deficit, a plummeting currency and decade-low economic growth.

To mark his appointment the Economic Times newspaper mocked up an image of him as fictional British Secret Service agent James Bond pointing a pistol made of Indian rupee notes.

Mr Rajan has successfully taken aim at inflation - bringing it down from double-digit levels to 5.4 per cent currently - and has been credited for creating a stable environment for the economy to grow.

India's economy expanded by 7.9 per cent in the fourth quarter of 2015-16, the fastest of any major economy.

Mr Rajan has also been praised for starting to tackle a mountain of bad bank loans.

"Overall Rajan has done a fantastic job and I am optimistic of his second tenure. The government will take a decision which is good for the Indian economy in the long run," Arun Singh, a senior economist at Dun and Bradstreet said.

Mr Rajan's good looks, suave demeanour and habit of providing a colourful quote have seen him amass a huge fan following among the general public.

He sent Twitter users aflutter last year when he told reporters after cutting interest rates that the snip wasn't meant to be a Diwali bonus and he was neither a hawk nor Santa Claus.

"My name is Raghuram Rajan and I do what I do," he declared, smiling.

In a sign of his popularity, almost 60,000 people have signed an online petition calling for him to be given a second term.

Yet his straight-talking has roiled some in India's right-wing government.

He ruffled feathers last year after wading into a debate about intolerance following the killing of a Muslim man suspected of eating beef - a taboo in the Hindu-majority nation.

Populist politician Subramanian Swamy has been leading a verbal onslaught against Mr Rajan, accusing the former University of Chicago professor of being "mentally not fully Indian", referring to his United States Green Card.

Mr Swamy also accused Mr Rajan of "wilfully and deliberately wrecking the Indian economy" - a claim most analysts agree is unfounded.

Mr Rajan has slashed interest rates over the past 18 months to their lowest level since early 2011 - but the BJP wanted deeper cuts to boost economic growth further.

Mr Rajan has maintained a dignified stand against the comments, telling NDTV: "My work shows my love for India".

A decision on Mr Rajan's future is not expected to be announced until August and some investors appear stirred, if not shaken, by the uncertainty.

The Indian stock market was jittery recently after a newspaper reported that Mr Rajan had sent a letter to Mr Modi telling him he wanted to return to the US to continue his academic work.

Mr Rajan denied writing such a note but has admitted openly that he sees his long-term future back in academia.

"Rajan is a good governor but the RBI institution is much stronger than one person," Sujan Hajra, chief economist at Anand Rathi securities said.

"If he goes, there will be an impact on investor sentiments but the systems in place at the RBI will ensure stability."